Here's a cool thing I posted on my math blog. It's in Norwegian, but I think you'll dig the short video.
I do math and music talks with a well-known Norwegian drummer. He's a really great guy. In this video he takes an African groove pattern and then layers a polyrhythm, every third beat and every fourth beat, and plays all three simultaneously with two hands and one foot. He illustrates this with a geometric pattern.
Here's the link. I didn't put it in the url field because I didn't want to scare you away with the foreign language. You can look at the pictures and then watch the 30 second clip.
http://matematikksenteret.no/content/4614/Polygoner-og-polyrytme
Is this based around Euclid's Algorithm?
If so, here's a very readable academic paper about it. If not, check out the paper anyway, 'cause it's cool stuff.
Ha! Thanks flagamuffin for the translate idea. I didn't think of that!
Here's the post in English... but the video doesn't seem to load on the translated page. Hrmph.
(Google translate has gotten pretty damn good, you know.)
PS Mike have you read How Not To Be Wrong? There's a really fascinating bit in there about some college students who used non-Euclidean geometry to break a Massachusetts state lottery. You'd dig it.